Carbon flashes in the heavy-element ocean on accreting neutron stars

We show that the burning of a small mass fraction of 12 C in a neutron star ocean is thermally unstable at low accumulated masses when the ocean contains heavy ashes from the hydrogen- burning rapid proton process. The key to early unstable ignition is the decreased thermal conductivity of a heavy- element ocean. The instability requires accretion rates, (M)over dot, in excess of 1/10 the Eddington limit when X-12 < 0.1. Lower (M)'s over dot will stably burn a small mass fraction of C-12. The unstable flashes release <similar to>10(42) -10(43) ergs over hours to days and are likely the cause of the recently discovered large type I bursts (the so-called superbursts) from six Galactic low- mass X-ray binaries. In addition to explaining the energetics, recurrence times, and durations of the superbursts, these mixed C-12 flashes also have an (M) over dot dependence of unstable burning similar to that observed. Although the instability is present at accretion rates approximate to (M) over dot (Edd), the flashes provide less of a contrast with the accretion luminosity there, thus explaining why detection is easier when (M) over dot (0.1-0.3) (M) over dot(Edd).